%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:06:52 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 17 unt; 2 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 28 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,equivalent(Y,X)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X1,X0)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X1,equivalent(X0,X2))))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f11,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X2,equivalent(X1,equivalent(X0,X2))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X3,equivalent(X2,X1)),X0)))),
inference(resolution,[status(thm)],[f11,f6]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X1))),equivalent(equivalent(X3,X2),X0)))),
inference(resolution,[status(thm)],[f11,f9]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),X3),equivalent(equivalent(X2,equivalent(X1,X0)),X3))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X3,equivalent(X2,X1)),X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f5]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(equivalent(X3,equivalent(X1,equivalent(X0,X3))),X2))),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X2,equivalent(X1,X0)),X3))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(resolution,[status(thm)],[f14,f5]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X2,equivalent(X1,X0)),equivalent(equivalent(X3,X4),equivalent(X5,equivalent(X4,equivalent(X3,X5))))))),
inference(resolution,[status(thm)],[f16,f9]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X3,equivalent(X1,equivalent(X0,X3))),X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f17,f5]) ).
fof(f45,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2)))),
inference(resolution,[status(thm)],[f22,f6]) ).
fof(f51,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X2,equivalent(X0,X1))))),
inference(resolution,[status(thm)],[f45,f8]) ).
fof(f65,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X2,equivalent(X2,equivalent(X0,X1))))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f51,f5]) ).
fof(f70,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(X2,X3)))))),
inference(resolution,[status(thm)],[f65,f45]) ).
fof(f138,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2))),equivalent(X3,X3))),
inference(resolution,[status(thm)],[f70,f8]) ).
fof(f411,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X3,X3))
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2)))) ),
inference(resolution,[status(thm)],[f138,f5]) ).
fof(f416,definition,
! [X0,X1,X2] :
( sQ0_spl
<=> ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f417,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2)))) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,definition,
! [X3] :
( sQ1_spl
<=> is_a_theorem(equivalent(X3,X3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X0,X0)) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f411,f416,f419]) ).
fof(f423,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f45]) ).
fof(f424,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X0))),equivalent(X2,X1))) ),
inference(resolution,[status(thm)],[f420,f30]) ).
fof(f586,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,X0)))) ),
inference(resolution,[status(thm)],[f438,f5]) ).
fof(f885,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))) ),
inference(resolution,[status(thm)],[f586,f25]) ).
fof(f1519,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X2,X0)))) ),
inference(resolution,[status(thm)],[f885,f8]) ).
fof(f2234,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f1519]) ).
fof(f2262,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f2234]) ).
fof(f2263,plain,
$false,
inference(sat_refutation,[status(thm)],[f422,f424,f2262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:06:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.56 % Refutation found
% 0.15/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.60 % Elapsed time: 0.224554 seconds
% 0.15/0.60 % CPU time: 1.114444 seconds
% 0.15/0.60 % Total memory used: 68.980 MB
% 0.15/0.60 % Net memory used: 67.059 MB
%------------------------------------------------------------------------------